RSA Public and Private key generation in Python

November 05, 2017

In this code, the only third-party library is "secrets" which is available to download and add automatically to python libraries by executing pip command.
for more information see post pip command.

-This program was written by Shooresh Sufiye. Feel free to copy and change it, But don't forget to mention the source.

# Written by Shooresh Sufiye
# RSA Algorithm Shooresh
from math import *
import random
import secrets

#===============-RSA key Class-==================
class RSAkey:
publicKey = []
PrivateKey = []
sp = 0
sq = 0
dig = 0
def __init__(self,sp,sq,length):
self.sp = int(sp)
self.sq = int(sq)
self.dig = int(length)
self.cal()

def getKeys(self):
keyl = []
keyl.append(self.publicKey)
keyl.append(self.PrivateKey)
return keyl
#+++++++++++++++++++-bigPrime Class-+++++++++++++++++++++++
class bigPrime:
P=None

def __init__(self):
self.P=None

def isPrime(self, a):
isp = None
b=int(sqrt(a))
# should change to stave algorithm or better !!!
while(b>1):
if(a%b==0):
isp = False
b=-1
break
else:
b-=1
if(b!=-1):
isp = True
print(".", end='')
return isp

def gimmi(self, dig, s): # Generat and get method for big prime numbers
pSeed = s
#p = random.SystemRandom (pSeed) # -for secure random number
p = int(random.random() * (10 ** dig))
p1 = p+(100 if (int(random.random() * 10)>5) else -100 )
if(p>p1): p,p1=p1,p
primesList=[]
primesList = [i for i in range(p,p1) if ((len(primesList)<=5) and self.isPrime(i))]
print()
p=random.choice(primesList)
primesList.remove(p)
self.P = p
return self.P

def egcd(self, a, b): # Extended Euclidean greatest common divisor
if a == 0:
return (b, 0, 1)
else:
g, y, x = self.egcd(b % a, a)
return (g, x - (b // a) * y, y)

def modinv(self, a, m): # mod inverse function
g, x, y = self.egcd(a, m)
if g != 1:
print('modular inverse does not exist')
else:
return x % m

#++++++++++++++++-end of bigPrime Class-++++++++++++++++++++++

def cal(self): # calculates RSA elements
b = self.bigPrime()
p = b.gimmi(self.dig, self.sp)
q = b.gimmi(self.dig, self.sq)
#print("P ",p,"Q ",q)
N = p*q
W = (p-1)*(q-1)
e = int(sqrt(W))
while(e<W):
if (gcd(W,e) == 1):
E = e
break
e+=1
d = (W / E)
d = E * int(random.random()*100)
D = b.modinv(E,W)
print("N ",N,"W ",W,"E ",E,"D ", D,"\nP ",p ,"Q ", q)
print("="*50)
print("public key: ( ",N,",",E," )")
print("Private key: ( ",N,",",D," )")
print("="*50)
self.publicKey = [N, E]
self.PrivateKey = [N, D]
#==============-end of RSA key Class-============
#================================================
# main part:
p=7 # input("Enter P seed? ")
q=11 # input("Enter Q seed? ")
length = input("How long digits key you want? ")
c = RSAkey(p,q,length)
print(c.getKeys())
input()